Doublestrike is single value, and mathematically works much like Strength, or the new Dodge. You can have various types of bonuses applying to doublestrike, similar to various types of bonuses to Strength: Competence, Morale, etc. Bonuses of the same type don't stack. Untyped bonuses generally stack (unless by some wild crazy chance the bonus really is typed and there's a bug in the text).

Doublestrike isn't like effects such as Flaming or Holy Burst, and can't trigger multiple times. It should be impossible to get Triplestrikes (or more!)... yet.